I went to Hajj with my young daughter, and I intended Tamattu‘ Hajj for her, but I did not slaughter because someone told me that it is permissible not to slaughter. What is the ruling on that?
Fatwa
All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that the Prophet Muhammad (saw) is His Messenger.
The one who performs the Tamattu’ Hajj is liable to slaughter a sacrifice if he is able. If he cannot, he should fast for three days in Hajj and seven days when he returns to his family. This applies to adults as well as children. As for children, their guardian should fast on their behalf. If anyone says anything other than that, he is mistaken.
Allah knows best.
Source: islamweb